{
  "id": "1811.07300",
  "version": "v2",
  "published": "2018-11-18T09:28:17.000Z",
  "updated": "2020-03-10T13:27:55.000Z",
  "title": "Large sieve with sparse sets of moduli for $\\mathbb{Z}[i]$",
  "authors": [
    "Stephan Baier",
    "Arpit Bansal"
  ],
  "comment": "18 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We establish a general large sieve inequality with sparse sets $\\mathcal{S}$ of moduli in the Gaussian integers which are in a sense well-distributed in arithmetic progressions. This extends earlier work of S. Baier on the large sieve with sparse sets of moduli. We then use this result to obtain large sieve bounds for the cases when $\\mathcal{S}$ consists of squares of Gaussian integers and of Gaussian primes. Our bound for the case of square moduli improves a recent result by the authors.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2020-03-10T13:27:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L40",
      "11N35"
    ],
    "keywords": [
      "sparse sets",
      "general large sieve inequality",
      "gaussian integers",
      "extends earlier work",
      "large sieve bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}